Question

the dotplot shows the heights (in inches) of the 25 students in mrs. nataros statistics class. (a) find the percentile for lynette, the student who is 65 inches tall. (enter an integer.) (b) ashers height is at the 88th percentile of the distribution. interpret this value. how tall is asher? ashers height is less than 12% of the 25 students in mrs. nataros statistics class. asher is 74 inches tall. ashers height is greater than 88% of the 25 students in mrs. nataros statistics class. asher is 88 inches tall. ashers height is greater than 88% of the 25 students in mrs. nataros statistics class. asher is 74 inches tall. ashers height is greater than 12% of the 25 students in mrs. nataros statistics class. asher is 63 inches tall.

Explanation:

Step1: Count number of values less than 65

Count the number of data - points to the left of 65 on the dot - plot. There are 5 values less than 65.

Step2: Calculate the percentile

Use the formula for percentile: $P=\frac{\text{Number of values less than the given value}}{\text{Total number of values}}\times100$. Here, the total number of values is 25. So $P = \frac{5}{25}\times100=20$.

Step3: Interpret 88th percentile

The $k$th percentile of a data set is the value such that $k$ percent of the data values are less than or equal to it. So if Asher's height is at the 88th percentile, his height is greater than 88% of the 25 students. Looking at the dot - plot, the value corresponding to a high percentile (close to 100) is 74 inches.

Answer:

(a) 20
(b) Asher's height is greater than 88% of the 25 students in Mrs. Nataro's statistics class. Asher is 74 inches tall.